TIKRIT, Iraq (CNN) --A U.S. military commander said the capture of Saddam Hussein is important, but not the "sole focus" of soldiers hunting down the guerrillas resisting and disrupting the U.S. occupation of Iraq.

Maj. Gen. Ray Odierno, commander of the 4th Infantry Division, says Saddam is "on the run" and believes "he's moving every three to four hours," making it impossible for him to direct guerrilla operations.

Hunting down the people who are the "command and control" for those operations is a major goal of U.S. troops, Odierno said.

"I don't think he (Saddam) is ordering any attacks on our soldiers," he said.

A total of 55 U.S. troops have been killed in hostile fire since May 1, when President Bush declared an end to major combat operations. Also since May 1, 62 U.S. troops have died in non-combat incidents, including accidents and illnesses. Since the start of the war, 255 U.S. troops have been killed -- 170 hostile deaths and 85 non-hostile.

Odierno said he hopes Saddam will eventually turn himself in, but he doubts that will happen -- and it would be better if soldiers captured, rather than killed, him.

"Would we like to take him alive if we catch him? Absolutely," Odierno said. "Let the people see we have captured him," he said.

Odierno said troops are following up daily tips about Saddam's whereabouts.